On the generation of clones containing near-unanimity operations |
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Authors: | Sebastian Kerkhoff |
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Institution: | 1.Institute of Algebra, TU Dresden,Dresden,Germany |
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Abstract: | It is a well-known consequence of the Baker-Pixley-Theorem that any clone containing a near-unanimity operation is finitely
generated, leading to the question what arity the generating functions must have. In this paper, we show that, for arbitrary
d ≥ 2 and large enough n, (n − 1)
d
− 1 is the smallest integer k such that, for every clone C on an n-element set that contains a (d + 1)-ary near-unanimity operation, C
(k) generates C. |
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Keywords: | |
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